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I have two time-courses. Both are the same length. Both are univariate. Each represents the average EEG signal from a unique subgroup. The two subgroups do not have the same number of subjects.

I would like to find individual time-points where the difference between the two groups is statistically significant.

It seems as though my options are:

  • Perform a two-tailed t-test for each time-point and correct for multiple comparisons.
  • Perform an ANOVA analysis.
  • Use a GLM to model each time-course and then analyze the beta coefficients

However, there seem to be drawbacks to each approach.

  • Given the length of the EEG time-course, and the relatively small difference between the two values, I worry about the risk of false negatives in the case of t-tests.
  • ANOVA can tell me if a given time-point is different, but does not identify the actual time-point of interest. Additionally, the assumption of independence would be violated because sequential measurements will be correlated.
  • Linear analysis would not identify time-points of interest.
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  • $\begingroup$ I asked this question about a very similar problem. In our case we have max 6 data points at any given time point, so there is a danger of false negatives. To try and use more of the data, I wondered if it's acceptable to fit a model and assess significant differences at a time point using that model fit. In our case there's strong evidence the model describes the time series. $\endgroup$ – R Greg Stacey Jun 2 '16 at 18:33
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Obviously super late with an answer here, but in case you haven't yet solved the issue, or you are working in the field and will face similar issues again... I would suggest adopting your first strategy and adjusting for multiple comparisons using a threshold-free cluster-enhancement technique followed by a maximum permutation test to correct for the comparisons.

Theoretical details with simulated EEG data can be found here

A user-friendly toolbox for matlab can be found here

Of course, when using permutation you are not limited to conducting a t-test and you could potentially use any sort of difference measure you see fit (with proper justification). That also entails that if you have multiple groups, or multiple factors using the F-values from the appropriate ANOVA as summary measures for your permutation would also work.

Good luck!

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